Difference between revisions of "Manuals/calci/INTERCEPT"
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| − | <div style="font-size:30px">'''INTERCEPT( | + | <div style="font-size:30px">'''INTERCEPT (KnownYArray,KnownXArray)'''</div><br/> |
| − | *<math> | + | *<math>KnownYArray</math> is the set of dependent data |
| − | * <math> | + | *<math>KnownXArray</math> is the set of independent data. |
| + | **INTERCEPT(),returns the intercept of the linear regression line. | ||
==Description== | ==Description== | ||
| − | *This function is calculating the point where the line is | + | *This function is calculating the point where the line is intersecting y-axis using dependent and independent variables. |
*Using this function we can find the value of <math> y </math> when <math> x </math> is zero. | *Using this function we can find the value of <math> y </math> when <math> x </math> is zero. | ||
*The intercept point is finding using simple linear regression. | *The intercept point is finding using simple linear regression. | ||
| Line 10: | Line 11: | ||
*Regression methods nearly to the simple ordinary least squares also exist. | *Regression methods nearly to the simple ordinary least squares also exist. | ||
*i.e.,The Least Squares method relies on taking partial derivatives with respect to the slope and intercept which provides a solvable pair of equations called normal equations. | *i.e.,The Least Squares method relies on taking partial derivatives with respect to the slope and intercept which provides a solvable pair of equations called normal equations. | ||
| − | *Suppose there are <math> n </math> data points <math> {y_{i}, x_{i}}</math>, where i = 1, 2, | + | *Suppose there are <math> n </math> data points <math> {y_{i}, x_{i}}</math>, where <math>i = 1, 2,...n</math> |
*To find the equation of the regression line:<math> a=\bar{y}-b.\bar{x}</math>. | *To find the equation of the regression line:<math> a=\bar{y}-b.\bar{x}</math>. | ||
*This equation will give a "best" fit for the data points. | *This equation will give a "best" fit for the data points. | ||
| Line 16: | Line 17: | ||
*The slope is calculated by:<math> b=\frac{\sum_{i=1}^{n} {(x_{i}-\bar{x})(y_{i}-\bar{y})}} {\sum_{i=1}^{n}{(x_{i}-\bar{x})}^2}</math>. | *The slope is calculated by:<math> b=\frac{\sum_{i=1}^{n} {(x_{i}-\bar{x})(y_{i}-\bar{y})}} {\sum_{i=1}^{n}{(x_{i}-\bar{x})}^2}</math>. | ||
*In this formula<math> \bar{x}</math> and<math> \bar{y}</math> are the sample means AVERAGE of <math> x</math> and <math> y </math>. | *In this formula<math> \bar{x}</math> and<math> \bar{y}</math> are the sample means AVERAGE of <math> x</math> and <math> y </math>. | ||
| − | *In <math>INTERCEPT( | + | *In <math>INTERCEPT (KnownYArray,KnownXArray)</math>, the arguments can be numbers, names, arrays, or references that contain numbers. |
* The arrays values are disregarded when it is contains text, logical values or empty cells. | * The arrays values are disregarded when it is contains text, logical values or empty cells. | ||
| − | *This function will return the result as error when any one of the argument is | + | *This function will return the result as error when any one of the argument is non-numeric or <math>x</math> and <math>y</math> is having different number of data points and there is no data. |
| − | |||
| − | + | ==ZOS== | |
| + | *The syntax is to calculate intercept of the regression line in ZOS is <math>INTERCEPT (KnownYArray,KnownXArray)</math>. | ||
| + | **<math>KnownYArray</math> is the set of dependent data | ||
| + | **<math>KnownXArray</math> is the set of independent data. | ||
| + | *For e.g.,intercept([14,16,19,15.25],[20.1,26,10,26.4]) | ||
| + | {{#ev:youtube|ltc2nl-pwpk|280|center|Intercept}} | ||
| − | + | ==Examples== | |
| + | {| class="wikitable" | ||
| + | |+Spreadsheet | ||
| + | |- | ||
| + | ! !! A !! B !! C !! D!! E | ||
| + | |- | ||
| + | ! 1 | ||
| + | | 4 || 5 || 2 ||10 || | ||
| + | |- | ||
| + | ! 2 | ||
| + | | 12 || 20 || 15 || 11 || | ||
| + | |- | ||
| + | ! 3 | ||
| + | | 25 || -12 || -9 ||30 ||18 | ||
| + | |- | ||
| + | ! 4 | ||
| + | | 10 ||15 || -40 ||52 ||36 | ||
| + | |} | ||
| − | + | #=INTERCEPT(A1:D1,A2:D2)= 10.13265306 | |
| − | + | #=INTERCEPT(A3:E3,A4:E4)= 4.754939085 | |
| − | |||
| − | + | ==Related Videos== | |
| − | + | {{#ev:youtube|LNSB0N6esPU|280|center|INTERCEPTS}} | |
| − | |||
| − | |||
| − | + | ==See Also== | |
| + | *[[Manuals/calci/PEARSON | PEARSON ]] | ||
| + | *[[Manuals/calci/AVERAGE | AVERAGE ]] | ||
| − | + | ==References== | |
| + | *[http://www.purplemath.com/modules/intrcept.htm INTERCEPT] | ||
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| − | + | *[[Z_API_Functions | List of Main Z Functions]] | |
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| − | + | *[[ Z3 | Z3 home ]] | |
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Latest revision as of 16:04, 1 August 2018
INTERCEPT (KnownYArray,KnownXArray)
- is the set of dependent data
- is the set of independent data.
- INTERCEPT(),returns the intercept of the linear regression line.
is the set of dependent data
is the set of independent data.
Description
- This function is calculating the point where the line is intersecting y-axis using dependent and independent variables.
- Using this function we can find the value of when is zero.
- The intercept point is finding using simple linear regression.
- It is fits a straight line through the set of points in such a way that makes vertical distances between the points of the data set and the fitted line as small as possible.
- Regression methods nearly to the simple ordinary least squares also exist.
- i.e.,The Least Squares method relies on taking partial derivatives with respect to the slope and intercept which provides a solvable pair of equations called normal equations.
- Suppose there are data points , where
- To find the equation of the regression line:.
- This equation will give a "best" fit for the data points.
- The "best" means least-squares method. Here b is the slope.
- The slope is calculated by:.
- In this formula and are the sample means AVERAGE of and .
- In , the arguments can be numbers, names, arrays, or references that contain numbers.
- The arrays values are disregarded when it is contains text, logical values or empty cells.
- This function will return the result as error when any one of the argument is non-numeric or and is having different number of data points and there is no data.
when 
is zero.
points in such a way that makes vertical distances between the points of the data set and the fitted line as small as possible.
, where 
.
.
and
are the sample means AVERAGE of 
, the arguments can be numbers, names, arrays, or references that contain numbers.ZOS
- The syntax is to calculate intercept of the regression line in ZOS is .
- is the set of dependent data
- is the set of independent data.
- For e.g.,intercept([14,16,19,15.25],[20.1,26,10,26.4])
Examples
| A | B | C | D | E | |
|---|---|---|---|---|---|
| 1 | 4 | 5 | 2 | 10 | |
| 2 | 12 | 20 | 15 | 11 | |
| 3 | 25 | -12 | -9 | 30 | 18 |
| 4 | 10 | 15 | -40 | 52 | 36 |
- =INTERCEPT(A1:D1,A2:D2)= 10.13265306
- =INTERCEPT(A3:E3,A4:E4)= 4.754939085
Related Videos
See Also
References